# Measuring effect size in ALDEx2

**Gloor lab musings**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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I’m in the throes of submitting a paper on effect sizes in ALDEx2, and so I thought I would take a stab at a nice concise blog post to summarize and simplify.

Effect sizes are standardized mean differences between groups, and are designed to convey what the experimentalist wants to know: how different are my groups given the treatment. In contrast, a very un-nuanced interpretation is that P-values provide a measure of whether the difference observed is due to chance or not.

More formally effect sizes measure the standardized mean difference between groups, and are equivalent to a Z score; how many standard deviations separate the mean of group 1 and group 2? Not surprisingly, effect size measures are very sensitive to the underlying distribution of the data. In datasets where it is not possible to assume normality, effect size measures are very difficult to generate and interpret.

In high throughput sequencing data the data are often not Normally-distributed as shown in the ‘Group Distribution’ plot which shows the density of the S:E:W:E feature in the ALDEx2 selex test dataset. The problem is how to find a sensible effect size for these two ugly data distributions.

Enter the ALDEx2 effect size measure which gives an estimate of the median standardized difference between groups. Note the wording, we take the media of the standardized group difference. How does this work?

If we have two distributions contained in two vectors

b = [b1, b2, … bm]

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**Gloor lab musings**.

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